Sol for 2 asset portfolio:
Since weights are given: 1=Wa+Wb therefore: wb=1-wa
σ2 = wa2σa2 + wb2σb2 + 2?wa?wb?σa?σb?ρ
substitute wb=1-wa
σ2 = wa2σa2 + (1-wa)2σb2 - 2?wa?(1-wa)?σa?σb
σ2 = wa2?0.12 + (1-wa)2?0.32 - 2?wa?(1-wa)?0.1?0.3
wa2?0.12 + (1-wa)2?0.32 - 2?wa?(1-wa)?0.1?0.3 = 0
Solve for wa (=3/4), then substitute into wb=1-wa to get Wa=3/4 ; Wb=1/4
2) By simplified formal definition "riskless" mean no risk thus variance would be zero, (as above, although in real world it's a bit different).
Therefore let's assume such riskless portfolio as benchmark, thus just calculate weighted return of portfolio:
Rf=(3/4)Ra + (1/4)Rb = 3/40 + 3/40 = 6/40 = 0.15 = 15%
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Answ:
1) wa=0.75 ; wb=0.25
2) Rf=15%
A market has two risky assets and one riskless asset.
1 Asset (A1) has a return of 6% and a risk of 10%.
The second asset (A2) has a return of 14% and a risk of 30%
The correlation between the returns of the two assets is - 1 (negative one)
What are the weights of a portfolio consisting of Asset 1 and Asset 2 only which has zero risk?
What is the return of the riskless asset in the market?
